Expression of type Equals

from the theory of proveit.numbers.summation

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import a, b, c, k
from proveit.core_expr_types import alpha_k
from proveit.logic import Equals
from proveit.numbers import Add, Interval, Sum, one

# build up the expression from sub-expressions
sub_expr1 = [k]
expr = Equals(Sum(index_or_indices = sub_expr1, summand = alpha_k, domain = Interval(a, c)), Add(Sum(index_or_indices = sub_expr1, summand = alpha_k, domain = Interval(a, b)), Sum(index_or_indices = sub_expr1, summand = alpha_k, domain = Interval(Add(b, one), c))))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(\sum_{k = a}^{c} \alpha_{k}\right) = \left(\left(\sum_{k = a}^{b} \alpha_{k}\right) + \left(\sum_{k = b + 1}^{c} \alpha_{k}\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 12 operand: 7
4	Operation	operator: 39 operands: 6
5	ExprTuple	7
6	ExprTuple	8, 9
7	Lambda	parameter: 31 body: 10
8	Operation	operator: 12 operand: 15
9	Operation	operator: 12 operand: 16
10	Conditional	value: 22 condition: 14
11	ExprTuple	15
12	Literal
13	ExprTuple	16
14	Operation	operator: 28 operands: 17
15	Lambda	parameter: 31 body: 18
16	Lambda	parameter: 31 body: 19
17	ExprTuple	31, 20
18	Conditional	value: 22 condition: 21
19	Conditional	value: 22 condition: 23
20	Operation	operator: 34 operands: 24
21	Operation	operator: 28 operands: 25
22	IndexedVar	variable: 26 index: 31
23	Operation	operator: 28 operands: 29
24	ExprTuple	36, 38
25	ExprTuple	31, 30
26	Variable
27	ExprTuple	31
28	Literal
29	ExprTuple	31, 32
30	Operation	operator: 34 operands: 33
31	Variable
32	Operation	operator: 34 operands: 35
33	ExprTuple	36, 41
34	Literal
35	ExprTuple	37, 38
36	Variable
37	Operation	operator: 39 operands: 40
38	Variable
39	Literal
40	ExprTuple	41, 42
41	Variable
42	Literal